Gamma-compactification of measurable spaces.
A space is truly weakly pseudocompact if is either weakly pseudocompact or Lindelöf locally compact. We prove that if is a generalized linearly ordered space, and either (i) each proper open interval in is truly weakly pseudocompact, or (ii) is paracompact and each point of has a truly weakly pseudocompact neighborhood, then is truly weakly pseudocompact. We also answer a question about weakly pseudocompact spaces posed by F. Eckertson in [Eck].
For a locally symmetric space , we define a compactification which we call the “geodesic compactification”. It is constructed by adding limit points in to certain geodesics in . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give for locally symmetric spaces. Moreover, has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...